Parents unknown. Y DNA testing shows that Luke Thornton does not match descendants of William Thornton.
Luke Thornton, of North Farnham Parish bern detached as son of William ‘the immigrant’ Thornton, Gent. & Alicia Thornton and relationships locked.
Be aware that posters at https://www.wikitree.com/wiki/Thornton-958 disagree that William is ruled out as father of Luke.
https://www.colonial-settlers-md-va.us/getperson.php?personID=I2523... Includes explanatory notes on DNA test result comparisons.
https://www.familytreedna.com/public/Thornton?iframe=yresults For DNA project groupings and STR comparison spreadsheet.